Math 235 does not have a common final exam.
If evaluating an external course for transfer credit, please see the comments at the bottom of the page.

 

RECOMMENDED TEXTBOOKS

Strang, Introduction to Linear Algebra (6th ed.)
Friedberg, Insel, Spence, Linear Algebra (5th ed.)
Lay, Lay, McDonald, Linear Algebra and Its Applications (5th ed.)

 

 

MEASURABLE OBJECTIVES

By the end of this course, students should be able to:

 

  1. Define and explain fundamental concepts in linear algebra, such as vectors, matrices, scalars, and vector spaces.
  2. Perform basic operations on vectors and matrices, including addition, subtraction, scalar multiplication, and matrix multiplication.
  3. Solve systems of linear equations using various methods, including Gaussian elimination and matrix inversion.
  4. Calculate the determinant of a matrix and understand how row operations affect the determinant.
  5. Determine the invertibility of a matrix and calculate matrix inverses using Gauss-Jordan technique.
  6. Comprehend the notion of vector spaces and be able to determine whether a set of vectors forms a vector space.
  7. Analyze the properties of vector spaces, including basis, dimension, linear independence, and span.
  8. Comprehend the definition of a linear transformation, and identify whether or not a given function is a linear transformation.
  9. Compute change-of-basis matrices and the matrix of a linear transformation.
  10. Decide whether or not a given linear transformation is injective or surjective, and compute its kernel and range.
  11. Use the Rank-Nullity Theorem to find information about a linear transformation between vector spaces.
  12. Identify several different inner products and use them to determine distance and angle in a given vector space.
  13. Understand orthogonality and compute components and projections of vectors.
  14. Apply techniques for finding eigenvalues and eigenvectors of square matrices and understand their significance in various applications.
  15. Use diagonalization to simplify and analyze complex systems and transformations.

 

 

ADDITIONAL APPPLICATIONS

Math 235 should reserve approximately 2-3 weeks or 6-9 lectures for concrete applications from their chosen textbook.  Individual instructors have wide freedom here.  Good choices of applications might include:

 

  • Orthonormal bases and the Gram-Schmidt algorithm
  • Least Squares Approximations
  • Types of matrices such as orthogonal matrices, unitary matrices, positive-definite matrices, etc.
  • Standard forms such as LU-factorization, Singular Value Decomposition, or Jordan Canonical Form
  • Markov Chains
  • Quadratic forms
  • Optimization
  • Applications to image compression
  • Applications to networks and linear programming

 

When evaluating external courses in transfer, a course that covers just the measurable objectives listed above may substitute for Math 235 and earn 3 units.  This is common for courses taken in quarter systems.  A course that contains additional applications as described here may earn 4 units.